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MS-9   Dec, 2009

MS-9 : Managerial economics

1. Distinguish between profit maximisation and value maximisation giving examples.

2 (a) Briefly explain the concept of price elasticity of demand giving suitable examples.

(b) What are the determinants of price elasticity ? Explain giving examples.

3. Write short notes on the following giving suitable examples :

a) Breakeven output level

b) Profit contribution analysis

(c) Operating leverage

4. Critically comment on the factors which determine the nature of competition giving suitable examples.

5 (a) Why will managers prefer to operate in a cartel type environment as opposed to

competition ? Explain.

(b) Sustaining collusion is difficult for firms. Explain why, with reference to the prisoners dilemma.

6.You are given to understand that the existing firm in a market drives 80% of its revenues from 20% of its customers. Your boss wants you to develop a strategy to enter this market to compete with the existing firm (incumbent). Your answer should focus on :

a)How you would target existing customers ?

b) How you would seek to attract new customers ?

c) It is possible that the incumbent will also change his strategy following your decision

to enter. How according to you will the incumbent react ?

d) What will be your counter strategy to combat the incumbent ?

7. What do you understand by 'laws of production ?   Explain the production function with one variable input highlighting the law of diminishing marginal returns and the stages of production

MS-9   Dec, 2010

MS-9 : Managerial economics

1. (a) Discuss the relation between the average product, marginal product and total product in the short run.

(b) How do these support the application of the law of variable proportion to the firm ? Give example.

2. (a) Why is the long run average cost curve called an "envelope curve" ?

(b) Business Managers say that the firm plans in the long run and operates in the short run. Elucidate.

3. (a) Identify the differences between price elasticity and income elasticity. Illustrate with the help of examples.

(b) Discuss the determinants of price elasticity. Give examples.

4. Write notes on any four of the following :

(a) Opportunity cost

(b) Incremental concept

(c) Barriers to entry

(d) Effect of advertisement on demand of a product

(e) Delphi technique

5. Write five important characteristics of perfect competition. Establish the profit 20

maximising output of a perfectly competitive firm in the short run.

6. State True or False and give reasons :

(a) If total profit is at a maximum, marginal profit is zero.

(b) If a good is normal, then both the substitution effect and the income effect cause quantity demanded to change in the same direction.

(c) If price elasticity of demand for a firm's output becomes more elastic, then the firm's marginal revenue will increase.

(d) If the price elasticity of demand for a firm's output is inelastic then the firm could increase its revenue by reducing price.

(e) Economies of scale is a short run concept.

7.Case study questions

(a) What is the difference in a shift in the demand curve and a movement along the

demand curve ?

(b) Discuss factors which cause the demand curve to shift upwards ?

(d) Will "price" and "income" have a similar effect on demand of vegetables ?

Explain.

MS-9   Dec, 2011

MS-9 : Managerial economics

1. One of the most significant business and economic trends of the late twentieth century

is the rise of 'global' or 'stateless'. Corporation critically comment on the statement taking examples from the real world firms.

2. (a) Discuss the concept and features of monopolistic competition giving examples.

(b) Explain which of the following markets could be considered monopolistically competitive. Give reasons for your answer.

(i) Automobiles

(ii) Restaurants

3. (a) Explain the concept of economies of scale.

(b) What are economies of scope ? How do they differ from economies of scale ?

4. For a demand function

P = 200 — 50Q

or Q = 400 — 2P

Calculate the point price elasticities when

(a) P =20 and Q = 180

(b) P = 80 and Q = 120

and determine whether the demand is elastic or inelastic.

5. (a) Discuss the marketing approach to a Demand measurement.

(b) Outline the trend projection method of demand forecasting with the help of an

illustration.

6. Read the following case problem and answer the questions given at the end.

HIGHWAY BLUES

Ratan Sethi opened a petrol-pump cum retail store on Delhi- Agra Highway, about two-hour drive from Delhi. His store sells typical items needed by highway travellers like fast foods, cold drink, chocolates, hot coffee, children's toys etc. He charges higher price compared to the sellers in Delhi, yet he is able to maintain brisk sale-particularly of "Yours' Special Pack" (YSP) consisting of soft drink in a disposable plastic bottle and a packet of light snacks. The Highway travellers prefer to stop at his store because, while their cars wait for petrol-filling they in the meantime can enjoy Your's Special Pack (and, in some cases would help themselves with some other items in the store).

Each year he could substantially enhance his sales by providing Special Summer Price

on YSP which is almost half of its regular price. Last year while returning from Delhi, Ratan found that a new, big and modern grocery shop has come up 15 kms from Delhi on the National Highway. It has affected his sales but only marginally. But last month another large convenience store has opened just , 5 km. away from his store. He knows that the challenge has come meet to his doorsteps and he expects to be adversely affected by the existence of these two stores.

He needs to meet this challenges and decides to use the pricing strategy which he has been using quite effectively till recently. He now permanently reduces the price of YSP to half of its existing price. But at the end of the year Ratan finds that his sales in general and of YSP in particular had declined by 20 per cent.

(a) Where has Ratan sethi gone wrong ?

(b) If he was a managerial economist, how do you think he would have handled the situation ?

Q 7. Break - even production of a firm is 5,000 units, its fixed cost is Rs. 50,000; the variable cost per unit Rs. 25. Find out the price of the product. How much the firm should produce to earn profit of Rs. 25,000 ?

MS-8   june, 2007

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1.Distinguish between decision making under certainty and decision making under uncertainty. Mention certain methods for solving decision problems under uncertainty. Discuss how these methods can be applied to solve decision problems.

2. Use Cramer's rule for a 3 x 3 system of linear equations to solve the following system :

2x - y + 3z =3

-x-y+3z= -6

x-2y-z= -2

3. From the data given below, compute the quartile deviation

4. The members of a Consulting firm rent cars from three rental agencies : 60% from agency l , 30% from agency 2 and 10% from agency 3. if   9% of the cars from agency 1 need a tune-up 20%. of the cars from agency 2 need a tune-up and 6% of the cars from agency 3 need a tune-up, what is the probability that a rental car delivered to the firm will need a tune-up ?

5. To see whether silicon chip sales are independent of where the US economy is in the business cycle, data have been calculated on the weekly sales of a firm and on whether the US economy was rising to a cycle peak, at a cycle peak, falling to a cycle peak or at a cycle trough. The results are

State the null hypothesis. At 0.10 significance level, what is your conclusion ?

(Given the tabulated value of test statistic is 10.645)

6. Write short notes on any three of the following :

(a) Concept of Maxima and Minima

(b) Types of classification of data

(c) Pascal Distribution

(d) Multi-stage sampling & Multi-phase sampling

(e) Box-Jenkins Models for Time Series

7. In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the Delhi half-marathon and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two-week period. What would be the null hypothesis ? Find

a 9o% confidence interval for the percentage of Delhi half-marathon runners who got sick in the two-weeks after the race.

8. A study by a roadways company on the effect of bus-ticket prices on the number of passengers produced the following results :

Develop the estimating equation that best describes the data. Predict the number of passengers per 100 miles if the ticket were Rs. 10.

MS-8   june, 2008

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. What factors       in modern society contribute to  the increasing importance of quantitative approach to  management ? List one applicaticn of quantitative techniques in each functional area of  management.

2. The demand for a certain product is represented by the equation p : 20 + 5q

-q2 where q is the number of units demanded and p is the price per unit. Find marginal revenue function. What is the marginal revenue at q = 2 ?

3 From the frequency distribution, find the standard deviation using the formula fcr the grouped data :

4. A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is ruste,C or a bolt ?

5. In a study to test whether there is a difference between the average height of adult females born in two different countries, random samples yielded the following results :

n1= 120 , mean of x1= 62.7 , and s1=2.5

n2= 150 , mean of x2= 61.8 , and s2=2.62

where the measurements significance to test the heights. are in inches. Use 0.05 level of difference between the  average heights

6. Write short notes on any threeof the following :

(a) Step functions

(b) significance of Measures of Dispersion

(c) Criteria of Optimism

(di The F disiribution

e)Auto-regressive (AR) models

7. Given below are figures of production (in thousand kilos) for a sugar factory. Obtain the secular trend by fitting a straight line.

8.Find the area under the standard normal curve, which lies

(a) to the left of z= 0.94

(b) to the right of z= 0.65

(c) to the right of z =1.76

(d) between z =0.34 and z =0.62

MS-8   june, 2009

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. An analysis of the hourly wages paid to workers in two firms A and B belonging to the same industry gives the following results :

2. Which firm, A or B pays out the larger amount as hourly wages ? In which firm A or B, is there greater variability in individual wages ? Bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is d.rawn

at random from one of the bags and is found to be red. Find the probability that it was drawn from bag A.

3.What do you understand by probability sampling ? Describe stratified and cluster sampling designs. Vhat is the difference between a cluster and a strata ?

4. A course in Quantitative Applications is taught to 12 students by conventional classroom procedure. A second group of 10 students was given the same course by programmed materials. The same examination was given to each Soup at the end of the course. The 12 classroom sfudents scored 85 marks on an average with the standard deviation 4, while 10 students using programmed material scored SL marks on an average with a standard deviation of 5. Test whether the two methods of learning are equally effective ? Use 0.10 level of significance.

5.The information given below relates to the advertisement and sales of a company (in lakhs of Rupee) :

Correlation coefficient between X & Y = 0.8

(a) Find the two regression equations.

(b) What should be the advertisement expenditure if the company wants to attain sales target of Rs 120 lakhs ?

6. Write short notes on any three of the following :

(a) Marginal Revenue

(b) Exponential Smoothing

(c) Less than type Ogive

(d) Probability densify tunction (pdf)

(u) Significance level

7. In a random sample of 500 people of a ctty, it was found that 160 preferred seafood. Find a 95% confidence interval for the actual proportion of people who preferred seafood.

8. Solve the following system of linear equations using matrices :

2x+3y+3z=5

x-2y+z= -4

3x-y-2z= 3

MS-8   june, 2010

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. A car is purchased for Rs. 300,000. If the depreciation for the first three years is at 10% per annum and for the next two years is at 20% per annum, then calculate the

depreciated value of the car at the end of five years.

2. Units A, B, C of a factory manufacture 25%, 35%, 40% respectively of the total cars.

Out of their output, 5%, 4%, 2% defective cars came from the units A, B, C respectively.

Using Baye's Theorem or otherwise, find the probability that a randomly selected car

found defective has come from the unit A.

3.Explain the term Random variable associated with an Experiment. Thereafter distinguish between discrete and continuous probability distributions also mentioning two discrete and two continuous distributions.

4. Compute the Quartile Q3, Decile D5, Percentile P50 and interpret these values in lines 1— 3 for the grouped data showing profits of 100 companies in a year in the table given below :

5. The breaking strength X of cables in a factory has a normal distribution with a mean of p.=1800 lbs and a standard deviation of v = 100 lbs. It is claimed that the breaking

strength X can be increased by the introduction of a new technique in the manufacturing

process. Should we accept the claim on the basis of a sample of 50 cables manufactured

under the new technique; at a significance level of a = .05 given that the mean breaking

strength for the sample is mean = 1850 with the standard deviation remaining the same.

(For convenience, we are giving the result P (Z <=1.645) = .95 where Z has the standard

normal distribution N (0,1)).

6. Write short notes on any three of the following topics :

a) Primary and secondary data

b) Arithmetic Mean and Median of data

c) Sample space associated with an experiment

d) Linear function

(e) Sampling with and without replacement explaining them, mentioning their scope, drawing graphs and giving examples wherever possible.

7. Using the method of least squares, find the regression equation of y on x for the data   given in the Table below :

And from the regression equation obtained, find the value of y corresponding to x = 2.5.

8. Solve the system of non-homogeneous linear equations :

x1 +x2 +2 x3= 2

3x1 — x2+ x3 = 6

-x1+ 3 x2 +4x3=4

by any one method out of cramar's rule, Inverse Matrix method, Gauss-Jordan method.

MS-8   june, 2011

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. You are given the frequency distribution of 292       workers of a factory according to their average weekly income. Calculate quartile deviation and its coefficient from the following data :

2. The Herr- McFee Company, which produces nuclear fuel rods, must X-ray and inspect each rod before shipping. Karen Wood, an inspector, has noted that for every, 1,000 fuel rods she inspects, 10 have interior flaws, 8 have casing flaws, and 5 have both flaws. In her quarterly report, Karen must include the probability of flaws in fuel rods. What is the probability ?

3. The manager of a small postal substation is trying to quantify the variation in the weekly demand for mailing tubes. She has decided to assume that this demand is normally distributed. She knows that on average 100 tubes are purchased weekly and that 90 percent of the time, weekly demand is below 115. What is the standard deviation of this distribution ?

4. The mean length of life of a certain cutting tool is 41.5 hours with a standard deviation of 2.5 hours. What is the probability that a simple random sample of size 50 drawn from this population will have a mean between 40.5 hours and 42 hours ?

5. Before an increase in excise duty on tea, 400 people out of a sample of 500 people were found to be tea drinkers. After an increase in duty, 400 people were tea drinkers in a sample of 600 people. State, whether there is a significant decrease in the consumption of tea. You may use a 5% level of significance.

6. Write short notes on any three of the following

(a) Central Limit Theorem

(b) Stratified Sampling

(c) Less than type Ogive

(d) Level of significance

(e) Coefficient of variation

7. Below are given the figures of production (in m. tonnes) of a sugar factory :

Estimate a linear trend equation and use it to forecast the production for 2009

8. The demand equation faced by DuMont Electronics for its personal computers is given by

P= 10,000 — 4Q, where P= price per unit and

Q= quantity demanded.

(a) Write the marginal revenue equation.

(b) At what price and quantity will marginal revenue be zero ?

(c) At what price and quantity will total revenue be maximized ?

(d) Find the price elasticity of demand at P = 6,000.

MS-8   Dec, 2007

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. Distinguish between decision making under certainty and decision making under uncertainty. Mention certain methods for solving decision problems under uncertainty. Discuss how these methods can be applied to solve decision problems.

2. Use Cramer's rule for a 3 x 3 system of linear equations to solve the following system :

2x - y + 3z = -3

-x-y+3z= -6

x-2y-z= -2

3. From the data given below, compute the quartile deviation.

4. the members of a consulting firm rent cars from three rental agencies : 60% from agency l, 30% from agency 2 and 10% from agency 3. if   9% of the cars from agency 1 need a tune-up , 20%. of the cars from agency 2 need a tune-up and 6% of the cars from agency 3 need a tune-up, what is the probability that a rental car delivered to the firm will need a tune-up ?

5. To see whether silicon chip sales are independent of where the US economy is in the business cycle, data have been calculated on the weekly sales of a firm and on whether the US economy was rising to a cycle peak, at a cycle peak, falling to a cycle peak or at a cycle trough. The results are

6. Write short notes on any three of the following :

(a) Concept of Maxima and Minima

(b) Types of classification of data

(c) Pascal Distribution

(d) Multi-stage sampling & Multi-phase sampling

(e) Box-Jenkins Models for Time Series

7. In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the Delhi half-marathon and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two-week period. What would be the null hypothesis ? Find a 9o% confidence interval for the percentage of Delhi half-marathon runners who got sick in the two-weeks after the race.

8. A study by a roadways company on the effect of bus-ticket prices on the number of passengers produced the following results :

Develop the estimating equation that best describes the data. Predict the number of passengers per 100 miles if the ticket were Rs.10.

MS-8   Dec, 2008

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

l. Explain Hypothesis testing. What are the steps involved in hypothesis testing ? Discuss the two types of .errors in testing of hypothesis

2. A telephone company in a town has 1000 subscribers on its list and collects a fixed charge of Rs. 400 per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Re.1one subscriber will discontinue the service. Find what increase will bring maximum revenue to the company.

3. A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's selection is l/5. What is the probability that

(a) both of them will be selected ?

(b) only one of them will be selected ?

(c) none of them will be selected ?

(d) at least one'of them will be selected ?

4. To test the effectiveness of training, a group of 5 participants were selected and given a test before and after the training. The result of the tests was as under:

Can the training be regarded as effective at 5 percent level of significance ?

5. An automobile company gives you the following information about age-groups and the liking for a particular model of car which is expected to be introduced :

On the basis of this data, can it be concluded that the model appeal is independent of the age-groups ?

(Given v = 3, and chi square at 0.05 = 7.815

6. Write short notes on any three of the following :

(a) Minor of an element of matrix

(b) Equally likely events

(c) Advantages of probability sampling

(d) Minimax criterion of decision making

(e) Standard deviation and standard error

7. Obtain the two regression equations for the following data using the method of least squares

8. Determine the sample size if sample standard deviation s = 6, population mean : 25, sample mean = 23 and the degree of precision is 99%.